Question

From a deck of cards, three cards are drawn on by one without replacement. Find the probability that each time it is a card of spade.

Answer 1

Consider the events
A = An ace in the first draw
B = An ace in the second draw
C = Getting an ace in the third draw

\[\text{ Now } , \]
\[P\left( A \right) = \frac{13}{52} = \frac{1}{4}\]
\[P\left( B/A \right) = \frac{12}{51} = \frac{4}{17}\]
\[P\left( C/A \cap B \right) = \frac{11}{50}\]
\[ \therefore \text{ Required probability }  = P\left( A \cap B \cap C \right)\]
\[ = P\left( A \right) \times P\left( B/A \right) \times P\left( C/A \cap B \right)\]
\[ = \frac{1}{4} \times \frac{4}{17} \times \frac{11}{50}\]
\[ = \frac{11}{850}\]